Automatic fixturing configuration is an important task to be addressed in manufacturing. An optimum clamping planning approach for arbitrarily shaped work-pieces based on computational geometry of contacting wrenches is developed. A clamping analysis algorithm drawing on the metric of force closure is presented, in which all feasible clamping points are automatically found by examining whether the convex hull of bounding wrenches associated with constraining contacts contains the origin. Optimal clamping points are then chosen from the feasible clamping regions according to a proposed criterion based on the radius of the maximal inscribed hypersphere centered at the origin within the convex hull. The clamping sequence is in turn decided by the feasible clamping area where the clamps are situated. A clamping equilibrium criterion is also proposed so that robust clamping layout can be generated. Case studies are included to demonstrate the effectiveness and capabilities of the developed methodology.